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The de-Broglie wavelength of a vehicle is $\lambda$. Its load is changed such that its velocity and energy both are doubled. Its new wavelength will be

Four uniform rods of mass $m\text{kg}$ each form a rectangle as shown in figure. The rods have negligible area of cross-section. Find the position of center of mass of the rectangle made up of the four uniform rods.

In the figure shown, there is a smooth tube of radius 'R', fixed in the vertical plane. A ball 'B' of mass 'm' is released from the top of the tube. B slides down due to gravity and compresses the spring. The end 'C' of the spring is fixed and the end A is free. Initially the line OA makes an angle of ${60}^{\circ }$ with OC and finally it makes an angle of ${30}^{\circ }$ after compression. Find the spring constant of the spring.

Two particles having masses $m_1$ and $m_2$ are situated in a plane perpendicular to line AB at a distance of $r_1$ and $r_2$ respectively as shown. Find the moment of inertia of the entire setup about an axis passing through system's centre of mass and perpendicular to line joining $m_1$ and $m_2$.

A person standing on an open ground hears the sound of a jet aeroplane coming from north at an angle ${60}^{\circ }$ with ground level. But he finds the aeroplane right vertically above his position. If $v$ is the speed of sound, then speed of the plane is

A particle of mass $m$ and charge $+q$ is midway between two fixed charged particles, each having a charge $+q$ and at a distance $2L$ apart. The middle charge is displaced slightly along the line joining the fixed charges and released. The time period of oscillation is proportional to

If the radius of earth be increased by a factor of $5$, by what factor its density be changed to keep the value of $g$ the same ?

Six moles of an ideal gas undergoes a thermodynamic cycle as shown in figure. If the temperatures are $T_A=600\text{K},T_B=800\text{K},T_C=2200\text{K}$ and $T_D=1200\text{K}$, the work done per cycle is approximately:

(Take universal gas constant, $R=\frac{25}{3}\text{J/mole. K}$)

A ball A moving with a certain velocity collides,with another ball B of the same mads at rrsr.If the coefficient of restitution is e,the ratio of the velocities of A and B just after collision is

A block of mass $m$ is placed on the floor of lift which is moving with velocity $v=4t^2$, where $t$ is time in second and velocity in $\text{m/s}$. Find the time at which normal force on the block is three times of its weight.

From the following $v^2$ - s graph. Find the displacement of the particle during the last 2 seconds.

A double slit of separation $0.1\text{mm}$ is illuminated by white light. A coloured interference pattern is formed on a screen $100\text{cm}$ away. If a pinhole is located in this screen at a distance of $2\text{mm}$ from the central fringe, the wavelengths in the visible spectrum $\left(4000\dot{\text{A}}\text{to}7000\dot{\text{A}}\right)$ which will be absent in the light transmitted through the pinhole is

A circular disc of radius $1\text{m}$ is rotating about an axis passing through its $COM$ and perpendicular to its plane. The moment of inertia about this axis is given by $I_{com}={\text{2 kg-m}}^2$. If the disc is rotated about an axis along its diameter, then the moment of inertia along that axis is $I_{dia}$. The value of $(I_{com}-I_{dia})$ is equal to

A force applied by an engine of a train of mass $2.05\times {10}^6\text{kg}$ changes its velocity from $5\text{m/s}$ to $25\text{m/s}$ in $5\text{minutes}$. The power of the engine is

In which of the following cases center of mass is not inside the body

In the figure shown, the total resistance between $A$ and $B$ is

A car moving at 108 km $h^{-1}$ finds another car in front of it going in the same direction at 72 km $h^{-1}$. The first car sounds a horn that has a dominant frequency of 800 Hz. What will be the apparent frequency heard by the driver in the front car? Speed of sound in air =$330m{s}^{-1}$

Which is these is a possible direction of acceleration for a point on a car that is going on a circular track and is speeding up?

On February 27, 1932 James Chadwick published his conclusive findings about the elusive neutron. Below is a representation of the experimental setup he used. What are the missing parts of the puzzle?

The same mass of copper is drawn into two wires $A$ and $B$ of radii $r$ and $3r$ respectively. They are connected in series, and electric current is passed. The ratio of the heat proiduced in $A$ and $B$ is :

A circular coil with its plane vertical is released from rest. It enters a region of a uniform magnetic field B at time $t=t_1$ and leaves the region at time $t=t_2$. The acceleration of the coil is

Find the frictional force between the two blocks. Take $g=10{\text{m/s}}^2$.

The main reason that a Flosbury flop was so efficient was

A string with one end fixed on a rigid wall passing over a fixed frictionless pulley at a distance of $2\text{m}$ from the wall, has a point mass $M=2\text{kg}$ attached to it at a distance of $1\text{m}$ from the wall. A mass $m=0.5\text{kg}$ attached at the free end is held at rest so that the string is horizontal between the wall and the pulley, and vertical beyond the pulley. What will be the speed which the mass $M$ will hit the wall when the mass $m$ is released? (Take $g=10{\text{m/s}}^2$)

A charge $2\mu \text{C}$ is taken from infinity to any point $P\text{(say)}$ in an electric field, without changing its velocity. If workdone against electrostatic forces is $-40\mu \text{J}$, then the electric potential at that point will be:

An automobile spring extends $0.2\text{m}$ for $5000\text{N}$ load. The ratio of potential energy stored in the spring to the potential energy stored in a $10\mu \text{F}$ capacitor at a potential difference of $10,000\text{V}$ will be

A series $\text{LCR}$ circuit connected across $(200\text{V},60\text{Hz})$ source. It consists of a capacitor of capacitive reactance $30\Omega$, a non-inductive resistor of $40\Omega$ and an ideal inductor of inductive reactance $90\Omega$ as shown in the figure. The value of inductance of the inductor in the circuit is nearly -





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